Quantum Mechanics and Atomic Orbitals
Bohr and Einstein particle nature of light
DeBroglie wave nature of particles
Schrödinger theoretical descriptions of atomsHeisenberg Dirac
quantum or wave mechanics
wave function =
every allowed e- state has unique
to calculate energy use Ĥ
Ĥ = E
solved for hydrogen wave functions
energies 2 = probability distribution
Ĥ = E
E
probability of finding an e- in Hat a particular distance from the nucleus
orbital
orbital requires 3 quantum numbersn l ml
principal 1, 2, 3, …size and energy
angular momentum
0, 1, 2, …, (n - 1)shape
magnetic-l, …, lorientation
“address”
orbital requires 3 quantum numbersn l ml
principal quantum number sizeenergy
as n increases orbitals become larger
e- is further from the nucleusn = 1n = 2n = 3n = 4n = 5n = 6n = 7
orbital requires 3 quantum numbersn l ml
angular momentum shape n - 1n = 1 l = 0n = 2 l = 0, 1n = 3 l = 0, 1, 2n = 4 l = 0, 1, 2, 3
designated by letters
l = 0 s orbitall = 1 p orbital
l = 2 d orbitall = 3 f orbital
0
n = 1 l = 0n = 2 l = 0, 1n = 3 l = 0, 1, 2n = 4 l = 0, 1, 2, 3
designated by letters
l = 0 s orbitall = 1 p orbital
l = 2 d orbitall = 3 f orbital
n = 1n = 2n = 3n = 4n = 5n = 6n = 7
sp
d
f
orbital requires 3 quantum numbersn l ml
magnetic quantum number -l,…, l
n = 1 l = 0 m = 0
n = 2 l = 0 m = 0
l = 1 m = -1m = 0m = 1
n = 3 l = 0 m = 0
l = 2
l = 1 m = -1m = 0m = 1
m = -2m = -1m = 0m = 1m = 2
row s
s
p
sp
d
1
1
3
3
1
51 s orbital3 p orbitals
5 d orbitals
1 s orbital3 p orbitals
5 d orbitals
n = 1n = 2n = 3n = 4n = 5n = 6n = 7
p
d
f
s
each orbital holds 2e- 4th quantum number ms
f orbitals7
spin
1s orbital
spherical
2
2s and 3s 2
1p orbital
2p orbitals 3dumbbell shape
3p, 4p, 5p etc. similar shapes larger
d orbitals3 5cloverleaf
larger n same shapes larger
Pauli exclusion principle
Polyelectronic Atoms
no 2 electrons same 4 quantum numbers
lowest energy orbitals fill first
1s orbital is lowest energy
H 1e- 1s1
He 2e- 1s2
which orbital fills next?
2s2p3s3p4s where is 3d?
1s 2s 2px 2py 2pz 3s 3px 3py 3pz 4s 3d 3d 3d 3d 3d
HHeLiBeBC
no! Hund’s rule parallel spins
NOF
Ne
Na [Ne]
K [Ar]4s 3dxz 3dxy3dyz 3dx2-z2 3dz2 4px
Ca [Ar]Sc [Ar]
Ti [Ar]
V [Ar]
Cr [Ar] no
half full shell stable
Mn [Ar]
Cu [Ar] no
full shell stable